Methods.:
A theoretical model was developed to describe the corneal cross-linking photochemical kinetics of Rf. After instillation with drops of Rf solution in distilled water, de-epithelialized porcine corneas were exposed to 365-nm ultraviolet light (UV-A) under varying irradiance and temperature. Oxygen concentration in the cornea at a known depth was monitored during UV-A illumination with a dissolved oxygen fiberoptic microsensor. Data from the oxygen experiments were used to confirm the model.

Results.:
On the basis of the known chemical reactions and diffusion rates of Rf and oxygen into the cornea, the authors developed a theoretical model consistent with corneal oxygen consumption experimental results during UV-A irradiation under different conditions. Oxygen concentration in the cornea is modulated by UV-A irradiance and temperature and quickly decreased at the beginning of UV-A exposure. The time-dependence of both Type-I and Type-II photochemical mechanisms in corneal cross-linking with Rf are discussed.

Conclusions.:
Using a chemical kinetics modeling approach, the authors developed a simple model that is in agreement with their experimental results on oxygen consumption in the cornea during corneal cross-linking with Rf. It is suggested that the main photochemical kinetics mechanism is the direct interaction between Rf triplets and reactive groups of corneal proteins, which leads to the cross-linking of the proteins mainly through radical reactions.

Introduction

Corneal cross-linking with riboflavin (Rf) is a technique that uses UV-A light and Rf to stabilize or reduce corneal ectasia, in diseases such as keratoconus and post-LASIK ectasia.1,2 Corneal cross-linking improves corneal strength by creating additional chemical bonds within the corneal tissue. The standard corneal cross-linking treatment uses a 30-minute instillation of drops (0.1% Rf in 20% dextran) every 3 to 5 minutes, followed by 30 minutes of 370-nm UV-A illumination at 3 mW/cm2 for 30 minutes (5.4 J/cm2 dose). The application of Rf drops is continued every 3 to 5 minutes during UV-A illumination. This procedure has been found to reduce corneal curvature greater than 1 diopter 1 year after treatment, with improvement persisting for 6 or more years.3 While the clinical benefits of this procedure are apparent, the underlying mechanisms remain poorly understood.

The common understanding is that exposure of Rf to UV-A light, in an oxygenated environment, causes the formation of singlet oxygen, which then acts on tissue to produce additional cross-linked bonds.4,5 The underlying molecular photochemical mechanisms of corneal cross-linking with Rf have been investigated in several studies,4–6 but the role of oxygen in this process, especially in modulating Type-I and Type-II photochemical kinetic mechanisms, is not well understood and remains speculative. Analysis of chemical kinetics, in addition to observed tissue oxygen concentrations, suggests that UV-A–excited molecules of Rf act as the predominant agent in corneal cross-linking. The purpose of this study was to simply model the photochemical kinetics of corneal cross-linking with Rf by using chemical constants found in the literature, and to confirm the model through measured oxygen concentration experiments under varying energy input conditions by UV-A irradiance and temperature modulation in ex vivo porcine cornea.

Methods

Theoretical Model

In the presence of light, Rf can exhibit photosensitizing properties, reacting with a wide range of electron-donating substrates (e.g., amines or amino acids) through mixed Type I–Type II photochemical mechanisms.7 In the Type I mechanism, which is favored at low oxygen concentrations, the substrate reacts with the sensitizer excited state to generate radicals or radical ions, respectively, by hydrogen atom or electron transfer. In the Type II mechanism, the excited sensitizer reacts with oxygen to form singlet molecular oxygen.

Some of the major kinetic reactions involved in Type I and Type II mechanisms are as follows.7–10

Common Reactions for Type I and Type II Mechanisms

Type I Mechanism

Type II Mechanism

In these reactions, Rf, Display Formula , and Display Formula represent riboflavin in the ground state, in the excited singlet, and triplet states, respectively; Display Formula , Display Formula , and RfH2 are the radical anion, the radical, and the reduced form of Rf, respectively; SH is the substrate and Display Formula , Display Formula , and Sox represent the intermediate radical cation, the radical, and the oxidized form of the substrate, respectively. Rfox is 7,8-dimethyl-10-(formylmethyl)isoalloxazine11 (unlike RfH2, it has UV-A absorption and sensitizer properties similar to Rf).

Now, if I0 is the amount of quanta of monochromatic light passing through a unit of surface during a unit of time, then the rate of the generation of Rf singlets, according to equations (1) to (3), can be expressed as:

where V and A are irradiated volume and area, t is time, NA is Avogadro's number, ε is molar extinction coefficient of Rf, αC is absorption coefficient of corneal stroma, and x is length of the absorbing pathway.

Assuming a steady state for Rf singlets, the expression for the reaction rate of Rf triplets becomes:

where Φ = k2/(k1 + k2) is the quantum yield of Rf triplets in the process described by equations (1) to (3).

Since unstable intermediates, such as excited Rf molecules, are assumed to be produced at a constant rate, and are rapidly degraded, leaving negligible concentrations, it is possible to assume a steady-state approximation for singlet and triplet Rf kinetics. The rate of change in concentrations for the rest of the participants in equations (1) to (8) can be summarized as follows:

where DRf and DO2 are the diffusion coefficients for Rf and oxygen in cornea.

The system of the equations (9) to (16) can be solved numerically by Euler's simple one-dimensional finite difference method and the Crank-Nicolson algorithm for partial differential equations, using the following initial and boundary conditions:

where t = 0 is the start of Rf instillation.

The assumption was made that the tissue is stable and is not swelling or thinning during UV-A illumination.

Photodegradation of Rf was neglected to simplify the model since the photolysis reaction rate at 3 mW/cm2 is relatively low, estimated at 1 × 10−2 to 2 × 10−2 min−1 by simple experiment. This means that approximately 1% of the Rf is degraded by photolysis during 30 seconds of irradiation. Earlier studies have reported the apparent first-order rate constants for the photolysis of Rf with UV-A as being 2.2 × 10−2 min−1 at a pH of 8.0 (Ahmed8) or ranging from 0.185 × 10−2 to 13.182 × 10−2 min−1 at pH 5.0 and 10.0 (Ahmad et al.11). At 30 mW/cm2 the exposure time was too short (not more than 15 seconds) to deplete Rf noticeably. By the authors' estimations, the rate constant at this irradiance is higher than the constants reported for 3 mW/cm2 irradiation, and approximately 4% of the Rf is degraded by photolysis during the initial 15 seconds. The assumption was made that Rf is being resupplied to the corneal surface during cross-linking (an infinite reservoir of fresh Rf) and that the two major photodegradation products of Rf (lumiflavin and lumichrome) act as photosensitizers,7 limiting the effect of photodegradation.

The variable inputs to this theoretical model were either derived from the literature or found through experimentation in the following sections (see Table 1).

Ratio between the rate constants of quenching Rf triplets by substrate and molecular oxygen

≈ 1

Lu et al.9; Gorner10

k4

Reaction rate between 2 Rf semiquinone radicals (RfH.)

3 × 108 M−1 s−1 (25°C), 9 × 108 M−1 s−1 (35°C)

Holmstrom36

The authors' fit*

k5

Reaction rate between 1,5-dihydroriboflavin and oxygen

1 × 103 M−1 s−1 (25°C), 3 × 103 M−1 s−1 (35°C)

Best-fit estimate†

k7

Singlet oxygen quenching rate constant, (reported for a derivative of DNA as quencher)

5 × 106 M−1 s−1 (25°C), 15 × 106 M−1 s−1 (35°C)

Lu et al.9

The authors' fit*

[O2]surf

Equilibrium concentration of oxygen in cornea before the experiments (below 100-μm flap)

7.3 mg/L (25°C), 4.7 mg/L (35°C)

As measured in this study

[SH]0

Concentration of the active substrate groups in cornea

1 mM

Best-fit estimate

* The authors' fit was based on the reaction rate's increase with temperature according to van't Hoff-Arrhenius observation.

† This reaction is a complex process and it can be slower or faster, modulated by the protein environment in which it is located; the slowest rate constant can be just several hundreds of the unit expressed as M−1 s−1 (Massey38).

Porcine Eyes and Corneal Flap Preparation

Porcine whole globes (Sioux-Preme Packing Co., Sioux City, IA; shipped overnight in saline solution packed in ice) were warmed to room temperature and allowed to become fully swollen. The corneas were then de-epithelialized with a dulled scalpel blade and corneal flaps were created by excision with an automated Hansatome microkeratome (model HT 230; Chiron Vision, Hansa Research & Development, Inc., Miami, FL). The average thickness of the flaps was approximately 100 μm, as measured with an ultrasonic pachymeter (DGH-550 Pachette 2; DGH Technology, Exton, PA).

Obtaining Diffusion Coefficients for Rf in the Cornea

The authors measured the diffusivity of Rf through experimentation by using a temperature-controlled (25°C and 37°C) Franz cell (PermeGear, Inc., Hellertown, PA). The corneal flaps were placed between the donor and receiver compartments of a series of Franz cells; the donor compartments were filled with an Rf solution of known concentration and the receiver compartments were filled with saline (Fig. 1). The amount of Rf passing through the corneal flaps per time was measured by means of spectrophotometry and the diffusivity of Rf was calculated by using Fick's first law.

Measurements of Oxygen Concentration during Corneal Cross-Linking with Rf

To estimate oxygen diffusivity in this study, the authors measured a change in oxygen concentrations under corneal flaps of known thickness. The experimental setup was enclosed in an incubator (model 12–140; Quincy Lab, Inc., Chicago, IL) to maintain temperature stability and measured with an attached K-type thermocouple (Chromel-Alumel general purpose thermocouple, model HH501DK; Omega Inc., Stanford, CT). Rf was applied to porcine globes by using a modified version of the method described by Spoerl et al.12 in which 0.1% riboflavin-5′-phosphate solution (Sigma Aldrich, St. Louis, MO) in distilled water was applied by drop (approximately 40 μL/drop) to the top of each cornea every 30 seconds for 20 minutes before cross-linking. A 50-μm diameter needle-type oxygen microsensor (NTH-PSt1-L2,5-TS-NS 20x0.40-YO; PreSens Precision Sensing GmbH, Regensburg, Germany) with a beveled stainless steel needle (outer diameter, 0.3 mm) was inserted under the flap needle bevel down, with the sensor's tip pulled slightly back under the needle's bevel tip. The needle's bevel tip shields the sensor from direct UV-A irradiation, preventing any direct interaction. Dissolved oxygen concentration data were recorded and stored with a fiberoptic oxygen meter (OXY-4 micro; PreSens). The experimental setup is shown in Figures 2 and 3.

Diagram of oxygen sensor being inserted under the corneal flap (thickness, 100 μm), UV-A source, and solution of Rf being administered to the corneal surface (thin film of Rf reaching up to 40 μm [Wollensak et al.37].

Figure 3.

Diagram of oxygen sensor being inserted under the corneal flap (thickness, 100 μm), UV-A source, and solution of Rf being administered to the corneal surface (thin film of Rf reaching up to 40 μm [Wollensak et al.37].

Corneas were pan-corneally irradiated with a top hat beam (±3% root mean square) for 30 minutes with a 365-nm light source (UV LED NCSU033B[T]; Nichia Co., Tokushima, Japan) at irradiances of 3 mW/cm2 or 30 mW/cm2 measured with a power sensor (model PD-300-UV; Ophir, Inc., Jerusalem, Israel) at the corneal surface, with three eyes for each irradiance. Riboflavin 0.1% in distilled water at the appropriate temperature, either 25°C or 35°C, was applied by dropper to the corneal surface during the time of irradiance every 30 seconds. The investigation was undertaken at both 25°C and 35°C, since most of the chemical rate constants used in this modeling were obtained from the literature (experiments conducted at 25°C) and that the average (clinically relevant) physiological temperature of the cornea is approximately 35°C.13 The authors were interested in understanding whether their kinetics model, in a fixed chemical system, was consistent with a range of experimental energy inputs.

In a separate experiment, the UV light was turned off after several minutes of irradiation for several light-dark cycles to observe light-mediated oxygen dynamics and to evaluate oxygen diffusivity in the cornea.

Controls

Two controls were evaluated to determine conditions required for observed oxygen consumption. The first control used a non-Rf–treated cornea illuminated with UV-A light for 30 minutes. This resulted in no detectable changes in oxygen concentration and verified that the UV-A light alone did not affect the oxygen sensor. The second control used Rf dissolved in distilled water. The solution was placed in a Petri dish with the oxygen sensor positioned 100 to 300 μm below the surface of the solution without the presence of corneal tissue. The solution was illuminated with UV-A light at 3 mW/cm2 for 30 minutes. No oxygen uptake was detected in this solution. An Rf solution with dextran was not chosen as a control because experiments under identical conditions showed oxygen consumption, which could potentially have complicated the analysis. These results suggest that the combination of Rf, UV-A, oxygen, and tissue are required for the detectable oxygen depletion seen in this system.

Results

The experimental results of the diffusion coefficients for Rf and oxygen are found in Table 1.

Rf diffusion coefficients of 4 × 10−7 cm2/s were obtained at 25°C and 6 × 10−7 cm2/s at 35°C for a 0.1% Rf solution in distilled water. These values are very similar to those found in the literature. Spoerl et al.12 have used a value of 6.5 × 10−7 cm2/s, on the basis of previously measured diffusion coefficient for sodium fluorescein. Because Rf and sodium fluorescein have similar polarity and molecular weight, it was assumed that the diffusivity of Rf would be similar. Araie and Maurice14 have reported diffusivity of fluorescein in rabbit corneas of 6 × 10−7 cm2/s at 37°C in an earlier study, and Nagataki et al.15 reported a value of (1.2 ± 0.2) × 10−6 cm2/s at 19°C (in this case, the value represents diffusion along [parallel to] the stroma and not across the stroma, as in our case). After a 20-minute instillation with Rf, the flap concentration at 100 μm was more than 80% of the Rf concentration applied at the corneal surface, and it was assumed that the Rf had reached a steady-state value, thus simplifying the theoretical calculations.

Illumination with UV-A irradiation caused a rapid (within several seconds) depletion of oxygen in Rf-containing cornea, and turning the UV light off led to replenishment of the oxygen to its original level within 3 to 4 minutes (Fig. 4). In these experiments, the observed period needed to reach a steady-state flow of oxygen through a corneal flap of known thickness matched expected oxygen diffusivity in the cornea. Oxygen diffusion coefficients of 4 × 10−6 cm2/s at 25°C and 6 × 10−6 cm2/s at 35°C were obtained. Diffusion of oxygen in the cornea has been studied by numerous authors. The diffusivity values vary because of their strong dependence on corneal hydration and temperature, which are difficult to control. A recent model for human corneal stroma reported by Larrea and Buchler16 uses an oxygen diffusion coefficient of 28 × 10−6 cm2/s (35°C), although earlier studies17–19 all have used an in vivo value close to 7 × 10−6 cm2/s. The oxygen diffusion coefficient for rabbit corneal stroma has been reported as (5 ± 1.8) × 10−6 cm2/s (25°C) by Takahashi et al.,20 and Harvitt and Bonnano21 have used a value close to 6 × 10−6 cm2/s in a later study.

Figure 5 shows the time-dependent depletion of dissolved oxygen below the 100-μm thick corneal flap with Rf cross-linking for a 3 mW/cm2 UV-A irradiance at 25°C and 35°C both theoretically and experimentally; the oxygen concentration (mg/L) fell to zero at 15 and 10 seconds, respectively. The theoretically modeled results were obtained by using parameters found in Table 1. The theoretical and experimental results correlated particularly well. (The mean square error [MSE] and the coefficient of determination [R2] were 0.14 and 0.98, respectively, for 25°C; 0.33 and 0.90, respectively, for 35°C).

Figure 6 shows the time-dependent depletion of dissolved oxygen below the 100-μm thick corneal flap with Rf cross-linking for a 3 mW/cm2 and 30 mW/cm2 UV-A irradiance at 25°C both theoretically and experimentally; the oxygen concentration (mg/L) fell to zero at 15 seconds and 5 seconds, respectively. The response time of the oxygen sensor was 2 seconds per data point, which limited the ability to correlate to the theoretical model. Again, the theoretically modeled results were obtained by using parameters found in Table 1. The theoretical and experimental results correlated particularly well, even with the response limits of the detector (for 30 mW/cm2, MSE = 0.64, R2 = 0.89).

Figure 7 shows the time-dependent depletion and gradual replenishment of dissolved oxygen below a 100-μm thick corneal flap with Rf cross-linking for a 3 mW/cm2 UV-A irradiance at 25°C. The oxygen concentration (mg/L) fell to zero at 15 seconds and gradually started to increase after approximately 10 minutes, getting back to approximately one-tenth its starting value after 30 minutes.

At 30 mW/cm2, a photodegradation reaction of Rf in this model was disregarded, as it seemed that it did not matter when comparing the model's result with the experimental data for the first 10 seconds of the irradiation (Fig. 6). Two major products of Rf photodegradation, lumiflavin and lumichrome, are reported to be less efficient than Rf in reaction with oxygen producing superoxide radical anions.22 Additionally, lumichrome has a 60% lower yield in producing singlet oxygen than riboflavin22 and therefore, the overall effect on oxygen depletion would be weaker in the authors' model, which maintained a steady Rf level and did not include generation of lumiflavin or lumichrome.

Discussion

A detailed understanding of the photochemical kinetic mechanisms of corneal cross-linking with Rf is still being developed. In the authors' modeling and experiments, oxygen was used as a proxy for measuring reaction kinetics. There are seemingly conflicting theories on the role of oxygen and, more specifically, whether singlet oxygen is the dominant photochemical kinetic mechanism.

Krueger et al.23 and Herekar24 have observed rapid oxygen depletion during corneal cross-linking with Rf and concluded that the reactive oxygen species (ROS), and specifically, singlet oxygen, are the predominant reaction drivers. McCall et al.4 have assumed that corneal cross-linking with Rf does not happen without carbonyl groups and singlet oxygen. This study used sodium azide to quench singlet oxygen selectively, but it has been reported before9,25 that this salt is also able to quench Rf triplets, which is the primary cross-linking reactant. McCall et al.4 have also found that the mean maximum destructive tension for clinical Rf UV-A–treated shark and rabbit corneas was enhanced with heavy water (D2O) because, as they cited, enhancement of singlet oxygen's half-life in heavy water ranges from 6.8 to 12 times. An alternative interpretation of their results, consistent with the authors' understanding, is that singlet oxygen does play a role (equations [7] and [8]) and would be enhanced under these very different conditions, but may not play the predominate role in standard clinical Rf UV-A cross-linking.

It has also been postulated that the role of UV-A irradiation in the presence of Rf is independent of singlet oxygen in causing collagen aggregation or photodamage of amino acids.25–27 Lu et al.9 and Gorner10 have shown that the competing role of singlet oxygen in these processes is not completely excluded but that the reactive path via singlet oxygen would not be the primary reaction.

Zhang et al.28 have reported that UV-A action in the presence of Rf can induce photo-oxidative damage of lysozymes under nitrogen atmosphere. It happens primarily because of the direct reaction between excited Rf triplets and tryptophan residues in the enzyme (a Type I mechanism). However, at low Rf concentrations, this pathway must be limited because, when Rf is illuminated anaerobically, its isoalloxazine ring becomes reduced10 and in order to restore it, some amount of oxygen is required.9 Furthermore, excess oxygen may be detrimental to the corneal cross-linking process because oxygen is able to inhibit free radical photopolymerization reactions by interacting with radical species to form chain-terminating peroxide molecules.29 For example, with increasing oxygen concentration, quantum yield of tryptophan photo-oxidation by Rf first increases and then decreases.30

Dynamics of the photo-induced oxygen uptake by the corneal matrix in this study suggest the following. Under aerobic conditions, which are present during the first 10 to 15 seconds of UV-A exposure, sensitized photo-oxidation of the substrate (proteoglycan core proteins and collagen in the corneal matrix) occurs mainly by its reaction with photochemically generated ROS, such as singlet molecular oxygen. This is consistent with a Type II photochemical mechanism. After the first 10 to 15 seconds, oxygen becomes totally depleted and the reaction between the substrate and Rf becomes consistent with a predominantly Type I photochemical mechanism. The authors' modeling is in good agreement with these experimental results. More than halfway through the period of illumination, the oxygen concentration in the cornea slowly increases to a concentration at which a Type-II mechanism may begin to play an additional role. During this phase, a growing contribution would be expected from the singlet oxygen–mediated cross-linking, together with the enhancement of secondary radical reactions that are modulated by oxygen.

The determined oxygen concentration profiles suggest reactions consistent with cross-linking in the layer of tissue interrogated by the oxygen sensor at 100 μm below the corneal surface. Although the detailed distribution and depth of corneal cross-linking with Rf remains under investigation, studies of corneal flaps taken at various depths after cross-linking, and tested by stress-strain behavior31 or sensitivity to collagen digestion,32 suggest that corneal stiffening is primarily in the anterior 200 μm of the corneal stroma. Increase of collagen fluorescence in UV-A–exposed corneas, which is related to their mechanical stiffening, can be detected at a depth 200 to 300 μm from the corneal surface.33

The authors believe that cross-linking in the cornea is initiated as a consequence of the direct interaction between the substrate and excited Rf triplets, with singlet oxygen playing a limited and transient role in the process. With an excess of Rf and low UV-A irradiation, there is no concern about the effect of the inactivation of Rf by reduction of its isoalloxazine ring, at least during the first few seconds of the procedure.

These experiments showed that if UV-A irradiation is stopped shortly after oxygen depletion, the rate of oxygen replenishment and the achievement of steady-state flow within the corneal flap are consistent with published oxygen diffusivity in the cornea.17–21 This suggests that dissolved free oxygen is significantly depleted not only at the position of the oxygen sensor and below, but also throughout the corneal flap above. Oxygen content in this scenario is therefore depleted throughout the cornea, by various chemical reactions, except for the very thin upper corneal layer where oxygen diffusion is able to keep up with the kinetics of the reactions. This diffusion-controlled zone will gradually move deeper into the cornea as the reaction ability of the substrate to uptake oxygen decreases.

Conclusion

Using a chemical kinetics modeling approach, the authors developed a simple model that is in agreement with their experimental results on oxygen consumption in the cornea during corneal cross-linking with Rf, under varying energy input conditions by UV-A irradiance and temperature modulation. The authors suggest that the main photochemical kinetics mechanism is the direct interaction between Rf triplets and reactive groups of corneal proteins, which leads to the cross-linking of the proteins mainly through radical reactions.

Oxygen measurements in the cornea monitored in this study support a predominant Type-I photosensitizing mechanism for corneal cross-linking with Rf after a very short initial Type II photochemical mechanism at the start of the illumination. More than halfway through the period of illumination, the oxygen concentration in the cornea slowly increases to a concentration at which a Type-II mechanism may begin to play an additional role.

Having established a new framework for the photochemical kinetics of corneal cross-linking with Rf, the authors plan to investigate the kinetics of free radial polymerization as the next step in enhancing the understanding of corneal cross-linking with Rf.

Diagram of oxygen sensor being inserted under the corneal flap (thickness, 100 μm), UV-A source, and solution of Rf being administered to the corneal surface (thin film of Rf reaching up to 40 μm [Wollensak et al.37].

Figure 3.

Diagram of oxygen sensor being inserted under the corneal flap (thickness, 100 μm), UV-A source, and solution of Rf being administered to the corneal surface (thin film of Rf reaching up to 40 μm [Wollensak et al.37].

Ratio between the rate constants of quenching Rf triplets by substrate and molecular oxygen

≈ 1

Lu et al.9; Gorner10

k4

Reaction rate between 2 Rf semiquinone radicals (RfH.)

3 × 108 M−1 s−1 (25°C), 9 × 108 M−1 s−1 (35°C)

Holmstrom36

The authors' fit*

k5

Reaction rate between 1,5-dihydroriboflavin and oxygen

1 × 103 M−1 s−1 (25°C), 3 × 103 M−1 s−1 (35°C)

Best-fit estimate†

k7

Singlet oxygen quenching rate constant, (reported for a derivative of DNA as quencher)

5 × 106 M−1 s−1 (25°C), 15 × 106 M−1 s−1 (35°C)

Lu et al.9

The authors' fit*

[O2]surf

Equilibrium concentration of oxygen in cornea before the experiments (below 100-μm flap)

7.3 mg/L (25°C), 4.7 mg/L (35°C)

As measured in this study

[SH]0

Concentration of the active substrate groups in cornea

1 mM

Best-fit estimate

* The authors' fit was based on the reaction rate's increase with temperature according to van't Hoff-Arrhenius observation.

† This reaction is a complex process and it can be slower or faster, modulated by the protein environment in which it is located; the slowest rate constant can be just several hundreds of the unit expressed as M−1 s−1 (Massey38).